Math Answers

The perimeter of a triangle is 60cm. Find the length of the sides of the triangle which gives a maximum area.

Determine the area under the standard normal distribution curve between z=1.15 and z=-1.85

Draw a Venn diagram to represent each of the following:

(a) AUB

(b) (AUB)

(c) An (BUC)

(d) (ANB) UC

(e) AnBnC

Let A = {x € N: 3 ≤ x ≤ 13}, B = {x € N : x is even}, and C = {x EN: x is odd}.

(a) Find An B.

(b) Find A UB.

(c) Find Bn C..

(d) Find BUC.

The lifetime of bulbs produced by Tariqs lightening company follows a normal distribution with a mean of 3462 hours and a standard deviation 1070 hours. What is the probability that randomly selected bulb will have a lifetime of at most 2800?

A merchant plans to sell two types of personal computers – a desktop model and a portable model that will cost Birr 25000 and Birr 40000 respectively. He estimates that the total monthly demand of computers will not exceed 250 units. Determine the number of units of each type of computers which the merchant should stock to get maximum profit if he does not want to invest more than Birr 70 lakhs and if his profit on the desktop model is Birr 4500 and on portable model is Birr 5000. (Find optimal Solution by simplex Model)

A credit card statement shows an unpaid balance of ₱6,300 on the billing date of September5. Changes and credits to the account are shown below. The finance charge at 2.3% on the average daily balance is entered on the billing date. Find the average daily balance, finance charge and the account balance on the next billing date, which is October 5. Credit Card Transactions: Sept. 10 purchase ₱3,205; Sept. 18 purchase of ₱4,750; Sept. 20 purchase of ₱9,000; and Oct. 1 payment of ₱20,000. Type your answer as: Average Daily Balance = ____________ Finance Charge = __________ Balance owed on October 5 = ____________

For each problem, find the equation of the line normal to the function at the given point. If the normal line is vertical line, indicate so. Otherwise, you answer should be in slope-intercept form.

1) y = -2x^2 - 4x at (-3, -6)

2) y = -x^3 + 2x^2 - 3 at (1, -2)

Mae purchased a home for ₱4,570,000 and obtained a 20-year loan with an annual interest rate of 8.5%, after paying a down payment of 25%. Find the the amount of interest paid on the loan over the 20 years

For each problem, find the equation of the line tangent to the function at the given point. Your answer should be a slope-form.

1) y = 2x^2 + 16x + 32 at (-3, 2)

2) y = (x-2)^(1/3) at (3,1)

3) y = -x^3 + 3x^2 -4 at (3, -4)

4) y = -3/ x^2 - 4 at (-1, 1)